Erratum: High-order strongly nonlinear long wave approximation and solitary wave solution (J. Fluid Mech. (20225) 945 ( A15) DOI: 10.1017/jfm.2022.544)

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doi:10.1017/jfm.2022.544, Published by Cambridge University Press, 18 July 2022 I have discovered that there was an error in one of the second-order equations (the evolution equation for φb) given by (5.12b) in Choi (2022), which will be hereinafter referred to as C22. The correct evolution equation for φb is given by(equation presented) (0.1) While the recursive formulas in C22 are correct, a mistake was made when the second-order model was simplified. As a result, the second-order evolution equation for v = φbx for one-dimensional waves given by (6.1b) in C22 is also incorrect. The evolution equation should read (equation presented). (0.2) Notice that the coefficient for vxvxx on the right-hand side has been changed to 3 from 5 in C22. The numerical results presented in figures 9, 11, and 12 in C22 are recomputed with the corrected second-order system, but the new numerical solutions are found close to the previous solutions as the error was introduced in the high-order dispersive terms of O(β4) ≪ 1. Therefore, no new numerical solutions are presented here although they are made available at It should be remarked that the maximum difference between the new and old solutions, for example, for the head-on collision of two-counter propagating solitary waves presented in figure 12 in C22 is found about 3.76 %. Therefore, the discussion about the second-order model in C22 remains valid. In the meantime, the loss of the truncated energy for the second-order model is found 0.179 % at t/(h/g)1/2 = 200 for the propagation of a single solitary wave presented in figure 9 and 0.198 % at t/(h/g)1/2 = 20 for the head-on collision of two solitary waves in figure 11, instead of 0.230 % and 0.130 %, respectively, reported in C22.

Original languageEnglish (US)
Article numberE2
JournalJournal of Fluid Mechanics
StatePublished - Dec 10 2022

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


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